Simulation Modeling

Introduction

Elizabeth King
Kevin Middleton

This Week

  • Simulating data for inference
    • Introduction to simulation modeling
    • Simulating null distributions: Beyond only sampling error
    • Approximate Bayesian Computation
    • Genetic Algorithms

Models

Models are simplifications of reality that help us to understand some aspect of our world

All models are false, but some are useful - George Box

Models do not investigate nature. Instead, they investigate the validity of our own thinking, i.e. whether the logic behind an argument is correct. … Once one begins to think of models as ‘thinking aids’ rather than investigations of natural phenomena, one could even go as far as to say that we only need models because our brains suffer from too many limitations, and are not able to consider all sides of a complicated argument in a balanced way. - Hannah Kokko in Modelling for Field Biologists and Other Interesting People

Generality vs Realism

Making a model is like making a map

Models tell you what will occur if the model’s assumptions are true

If:

  • there is no difference in two groups
  • the variable of interest is normally distributed
  • you randomly sample 20 from each group

Then:

  • you can predict exactly what outcomes will occur with some probability

Types of Models

  • Analytical models
  • Simulation models

Statistical Inference as Modeling

Remember the Goal of Statistics

“a way of taming uncertainty, of turning raw data into arguments that can resolve profound questions” (Amabile 1989)

  • The statistical analyses that you carry out are models.
  • Inference depends on evaluating the relative support for different models.

Example: Wing Dimorphic Crickets

Do long-winged crickets have a higher resting metabolic rate than short-winged crickets?

Controlling for body mass,

  • Metabolic rates do not differ
  • Average metabolic rate of long-wings is higher
  • Average metabolic rate of long-wings is lower

Statistical Inference as Modeling

Many problems are more easily (or possibly) solved without a traditional likelihood

  1. Simulate your own null distribution to test your hypothesis
  2. Sample from distributions and compare to observed values (Approximate Bayesian Computation)
  3. Generate “populations” of parameters and let them “evolve” across generations (Genetic Algorithm)

References

Amabile, T. 1989. Against All Odds Inside Statistics. Annenberg/CPB Collection; Intellimation [distributor].